Lines and Angles Definitions

Adjacent lines (two angles with same vertex)

complementary angles (two angles that equal 90 degrees)

supplementary angles (two angles measure 180 degrees)

linear pair (two angles that are adjacent + supplementary)

vertical angles (angles opposite of each other when two lines intersect)

perpendicular lines (two lines that make a 90 degrees angle)

transversal (a line that cuts across two or more lines in diff points)

corresponding angles (two angles that are in the same relative position when a transversal line cuts through two or more lines {doesn't have to be equal})

alternate interior angles (two angles that lie on opp sides of transversal but lie oninteriors of lines cut by transversal)

alternate exterior angles (two angles that lie on opp sides of transversal but lin on exteriors of lines cut by transversal)

same side interior angles (two angles that lie on the same side of transversal but lie on interiors of lines cut by transversal)

same side exterior angles (two angles that lie on the same side of transversal but lie on exteriors of lines cut by transversal)

when lines are parallel w transversal and angles are congruent….

set equal to each other

when lines are parallel w transversal and angles are supplementary….

add and set equal to 180 degrees

slope from two points:

y2-y1/x2-x1

distance formula:

d=√(x2−x1)²+(y2−y1)²

midpoint formula:

(x1+x1/2) , (y1+y2/2)

sum of angles in a quadrilateral equals…

360 degrees

parallelogram

a quadrilateral where both pairs of opposite sides are parallel

6 properties of a parallelogram are…

1. opp sides are parallel

2. opp sides are congruent

3. diagonals of a parallelogram bisect each other

4. opposite angles in a parallelogram are congruent

5. consecutive angles are supplementary

6. each diagonal of a parallelogram separates it into two congruent triangles

ASS and AAA are the only tri cong properties that don't work

ASS and AAA are the only tri cong properties that don't work

distances are always….(positive, negative)

positive

isosceles

two sides of the same length

slope is undefined if….

denominator is 0

consecutive angles

angles that are on the same side of the transversal (ex. bottom two angles of a trapezoid )

legs

nonparallel sides of a isosceles trapezoid

trapezoid def

a quadrilateral with exactly 1 set of parallel lines

4 properties of a isosceles trapezoid:

1. non parallel sides are congruent 

2. diagonals are congruent

3. base angles are congruent

4. consecutive angles of the legs are supplementary

5. 

median (of a trapezoid)

segment that connects midpoints of both legs

median (trapezoid) formula:

median = 1/2(length of base + langeth of top)

median of a triangle

line segment from vertex to midpoint of base

altitude of a triangle

line segment from vertex that is perpendicular to the other side

3 medians of a triangle intersect at the…

centroid

3 perpendicular bisectors of a triangle intersect at the…

circumcenter

3 angle bisectors of a triangle intersect at the…

incenter